This project continues to focus on the formulation, analysis, and biophysical interpretation of mathematical models which describe various aspects of neuroelectric signaling for individual neurons. Among the topics of current interest are: (i) integration of synaptic input delivered to the soma and dendritic branches of a neuron; (ii) steady propagation of action potentials along axons; (iii) stimulus-response and threshold properties for repetitive-firing of action potentials. Mathematical models of these phenomena involve systems of linear and nonlinear ordinary differential equations and parabolic partial differential equations. Solutions and their mathematical stability are determined by analytical and numerical methods. One aspect in the approach of this project is to expose the qualitative mathematical structure for classes of models by exploiting simple, yet reasonable, equations. Because qualititatively related mathematical problems arise in other biological and chemical context, e.g. chemical and biochemical oscillations, this project may consider models from such applications.